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Year 11
Foundation

Volume of composite solids

I can calculate the volume of a composite solid.

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New
New
Year 11
Foundation

Volume of composite solids

I can calculate the volume of a composite solid.

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. A composite solid can be decomposed to make the volume easier to calculate.
  2. Completing the solid may be a more useful method.
  3. Decomposing and rearranging parts of the solid may be beneficial.

Common misconception

Pupils may only using given measures in their calculations, even when these are not the lengths required for substitution into a volume formula.

Encourage pupils to annotate diagrams to show how the are breaking down a compound/composite shape. Pupils should label the diagram with any new lengths needed. They may need to use Pythagoras or trigonometry to find these new lengths.

Keywords

  • Volume - The volume is the amount of space occupied by a closed 3D shape.

  • Compound shape - A compound shape is a shape created using two or more basic shapes. A composite shape is an alternative for compound shape.

If some of the measurements are given in different units of length (such as cm and m), encourage the pupils to convert the lengths to the same unit, before starting the volume calculation.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Starter quiz

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6 Questions

Q1.
A shape created using two or more basic shapes is called a shape.
Correct Answer: composite, compound
Q2.
This composite solid is constructed from two cuboids. All lengths given are in centimetres. Calculate the total surface area of the solid.
An image in a quiz
456 cm²
912 cm²
Correct answer: 952 cm²
982 cm²
Q3.
This composite solid is constructed from two congruent cuboids. All lengths given are in centimetres. The total surface area of the solid is cm².
An image in a quiz
Correct Answer: 168
Q4.
The composite solid is constructed by placing a hemisphere with diameter 8 cm on top of a cuboid. Find the surface area of the solid.
An image in a quiz
206 cm²
Correct answer: 306 cm²
357 cm²
407 cm²
Q5.
The composite solid is constructed with a cylinder and a hemisphere. Each have a diameter of 12 cm. Find the surface area of the solid.
An image in a quiz
792 cm²
829 cm²
867cm²
Correct answer: 905 cm²
1018 cm²
Q6.
The composite solid is constructed with a cone and a hemisphere. The surface area, in terms of 𝜋, is 𝜋 cm².
An image in a quiz
Correct Answer: 72

Exit quiz

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6 Questions

Q1.
The amount of space occupied by a closed 3D shape is called the of the shape.
Correct Answer: volume
Q2.
The diagram shows a composite solid constructed from two congruent cuboids. All lengths given are in centimetres. Which of these calculations give the total volume of the solid?
An image in a quiz
Correct answer: 4 × 8 × 2 + 4 × 2 × 4
Correct answer: (2 × 6 + 6 × 2) × 4
4 × 2 × 8 + 2 × 4 × 8
6 × 4 × 8
Correct answer: 2 × 6 × 4 × 2
Q3.
This composite solid is constructed from two cuboids. All lengths given are in metres. The total volume of the solid is m³.
An image in a quiz
Correct Answer: 360
Q4.
This composite solid is constructed by placing a hemisphere with diameter 12 cm on top of a cuboid. Find the volume of the solid. Give your answer to the nearest cubic centimetre.
An image in a quiz
631 cm³
Correct answer: 932 cm³
1385 cm³
4099 cm³
Q5.
This composite solid is constructed with a cylinder and a hemisphere. Each have a diameter of 8 cm. The volume of the solid is cm³ (correct to 3 significant figures).
An image in a quiz
Correct Answer: 737
Q6.
This composite solid is constructed with a cone and a hemisphere. The volume of the solid, in terms of 𝜋, is 𝜋 cm³.
An image in a quiz
Correct Answer: 891